Prism-coupling techniques can be used to measure the spectrum of guided modes of a planar optical waveguide to characterize the waveguide properties, e.g., to measure the refractive index and stress profiles. This technique has been used to measure the stress and the depth-of-layer (DOL) of different ion-exchanged (IOX) glasses.
Certain types of IOX glasses are actual dual IOX (DIOX) glasses formed by first and second diffusions that give rise to a two-segment profile. The first segment is adjacent the surface and has a relatively steep slope, while the second segment extends deeper into the substrate but has a relatively shallow slope. Such DIOX profiles are formed in certain types of chemically strengthened glasses and anti-microbial glasses.
Such two-segment profiles result in a relatively large spacing between low-order modes, which have a relatively high effective index, and a very small spacing between high-order modes, which have a relatively low effective index. This difference in mode spacing is further enhanced when a conventional coupling prism, which has an output-side angle α of about 60°, is used. For such a coupling prism, angular sensitivity of exit rays is higher for the low-order modes than for the high-order modes. The spacing between modes is of interest since the modes are detected by a photodetector (i.e., a digital camera). The resolution of the measurement is defined by the number of photodetector pixels between adjacent modes.
By way of example, consider a typical refractive index profile of a DIOX glass formed using Ag+ (shallow) and K+ (deep) diffusions. The steep, shallow Ag+ IOX region can have an index variation of about 0.06 and a depth of about 3 μm from the glass surface. The shallower but deeper K+ IOX region can have a substantially smaller index variation of only about 0.01 and a depth of about 90 μm from the glass surface. The spacing between the lowest-order two (TE or TM) modes at the photodetector can be many hundreds of pixels, while the spacing between the highest-order two modes may be only a few pixels.
This distribution of the modes over the photodetector pixels is problematic when precise measurements of the deeper segment of the DIOX profile are sought because the high-order modes that travel in the deeper segment are under-sampled. If the DOL is large enough, it becomes impossible to adequately resolve the spectral lines of high-order modes, and as a result the DIOX profile cannot be precisely measured.
One option for obtaining the required measurement resolution is to have a larger photodetector with more pixels, which in some cases may also require a larger-aperture optical system. However, such photodetectors and larger-aperture optical systems add substantial cost and complexity to the measurement system.